Attributive concept descriptions with complements
Artificial Intelligence
Reasoning about knowledge
Reasoning in description logics
Principles of knowledge representation
Combining Terminological Logics with Tense Logic
EPIA '93 Proceedings of the 6th Portuguese Conference on Artificial Intelligence: Progress in Artificial Intelligence
Terminological logics with modal operators
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
A Temporal Description Logic for Reasoning over Conceptual Schemas and Queries
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Tableaux for Temporal Description Logic with Constant Domains
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Description logics for relative terminologies
ESSLLI'08/09 Proceedings of the 2008 international conference on Interfaces: explorations in logic, language and computation
ALCALC: a context description logic
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
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In this paper, we construct a new concept description language intended for representing dynamic and intensional knowledge. The most important feature distinguishing this language from its predecessors in the literature is that it allows applications of modal operators to all kinds of syntactic terms: concepts, roles and formulas. Moreover, the language may contain both local (i.e., state-dependent) and global (i.e., state-independent) concepts, roles and objects. All this provides us with the most complete and natural means for reflecting the dynamic and intensional behaviour of application domains. We construct a satisfiability checking (mosaic-type) algorithm for this language (based on ALC) in (i) arbitrary multimodal frames, (ii) frames with universal accessibility relations (for knowledge) and (iii) frames with transitive, symmetrical and euclidean relations (for beliefs). On the other hand, it is shown that the satisfaction problem becomes undecidable if the underlying frames are arbitrary linear orders or the language contains the common knowledge operator for n ≥ 2 agents.